Apartments with cracked walls, prehistoric floors, Eisenhower-era décor and a half-built cantilevered floor (for an extra bedroom) don’t usually go on the market for $6 million.

But in New York City, the right provenance can make up for almost anything.

A two-floor, three-bedroom penthouse at 530 East 72nd Street, which Frank Sinatra helped design when the building went up in 1961; then lived in with his much-younger bride, Mia Farrow; then sold to Andy Warhol’s physician, Denton S. Cox, is being put on the market by the doctor’s estate this Friday for $5,995,000.

The listing brokers are Halstead’s Ann Bialek and Nicholas Guider.

In his 35 or so years there, Cox didn’t keep the place in aristocratic condition, and he never combined the main penthouse apartment with Sinatra’s upstairs space for singing and partying, called the conservatory. “He had one architect that worked with him for a year or two,” said Cox’s sister, Patty Mansfield. “He was never satisfied, and then he got another one. … You have to understand the kind of mind that works that way: An admirable eccentricity! Or something like that.”

When Cox died last year at age 79, he had been building a cantilevered floor in the 18-foot-high conservatory to make an extra bedroom, and had drafted plans for connecting the two units. Meanwhile, the main apartment didn’t get upgraded: “There was no point in redecorating any of it, painting or redoing the parquet floors, which need it very much,” his sister said, “because he was going to redo everything as he connected the two.”

On the other hand, the lifelong bachelor filled the 3,000-square-foot spread, its massive wraparound terrace and its private roof space with plants, trees, lights and art: “I think Andy Warhol referred to it as ‘your wonderful glittering thing in the sky,’” Ms. Mansfield said.

Besides Warhol, Cox tended to John Steinbeck, King Hussein of Jordan and Judy Garland, his sister said. Then there was Sinatra, who met Cox some time in the late 60’s after falling ill: The physician was called up to the penthouse from his own ground-floor medical practice in the building.

He bought the penthouse around 1972. “There are wallpapers and tiles and flooring that Sinatra put in; my brother never changed any of that,” Ms. Mansfield said. What do they look like? “Awful! I mean, they’re 1961.”

As for the linoleum kitchen floors: “It’s just the way Sinatra had it. It’s just amusing at this point.”

And the walls: “They’re not falling down, they just have cracks and things.”